Well, there are some more places in a few side streets of Capitol, the big building at the end of state street.
Apart from that there aren't really any clusters I would say, though individual places definitely.
I don't want to be negative but if you are from NYC and you are already afraid now of going stir crazy then I wouldn't be surprised if you actually do.
I went to Madison only one semester as a foreign exchange student and I had that experience a little.
You will have a hard time finding trendy bars or places to get things like good sandwiches a la Carnegie Deli, John's Pizzeria, etc.
You can get quite a lot of ethnic food but I can prepare a better pasta than the Italian restaurants there. The positive side about bars is that you can get very cheap booze, expect zip in terms of style though.
And yeah, most people in Madison are really full of State Street and think it's truly amazing, so that might give you some perspective.
I hope I don't sound too negative, it's not that bad of a place either, but the threat has been a little too positive imo so far.